{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MUZalsPh_leQ"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/oughtinc/ergo/blob/master/notebooks/el-paso-workflow.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is Ergo?\n",
    "We believe that many of the pieces for good forecasting work exist, but are difficult to connect in a productive workflow. We think that building better infrastructure for forecasting can help create more scalable, high quality forecasting. \n",
    "\n",
    "Ergo provides part of that infrastructure. It's a python library for integrating model-based and judgmental forecasting. Currently, it provides an easy way to create and combine probability distributions, as well as predictions from community predictions sites like Metaculus, to help produce more accurate judgments. \n",
    "\n",
    "To showcase this, we've put together an example use case for predicting max ventilator use in El Paso below. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SRfoXVe2_leU"
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GmLVVio5_leY"
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "!pip install --progress-bar off poetry\n",
    "!pip install --progress-bar off git+https://github.com/oughtinc/ergo.git@e9f6463de652f4e15d7c9ab0bb9f067fef8847f7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9x_IOXYZ_lep"
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "import ssl\n",
    "warnings.filterwarnings(action=\"ignore\", category=FutureWarning)\n",
    "warnings.filterwarnings(action=\"ignore\", module=\"plotnine\")\n",
    "ssl._create_default_https_context = ssl._create_unverified_context"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9KSi5XYc_le1"
   },
   "outputs": [],
   "source": [
    "import ergo\n",
    "import seaborn\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from datetime import timedelta, date\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "pd.set_option('precision', 2)\n",
    "\n",
    "def summarize_samples(samples):\n",
    "    stats = samples.describe(percentiles=[0.05, 0.5, 0.95])\n",
    "    percentile = lambda pt: float(stats.loc[f\"{pt}%\"])\n",
    "    return f\"{percentile(50):.2f} ({percentile(5):.2f} to {percentile(95):.2f})\"\n",
    "\n",
    "def show_marginal(func):\n",
    "    samples = ergo.run(func, num_samples=1000)[\"output\"]\n",
    "    seaborn.distplot(samples).set_title(func.__doc__);\n",
    "    plt.show()\n",
    "    print(f\"Median {func.__doc__}: {summarize_samples(samples)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "VPlIqr_6_lfG"
   },
   "source": [
    "# Choose a decision-relevant question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WGzLvASO_lfJ"
   },
   "source": [
    "## How many ventilators will be needed in El Paso?\n",
    "\n",
    "I want to predict the answer to this question:\n",
    "\n",
    "> In El Paso, what is the maximum number of ventilators needed for COVID patients on a given day in May?\n",
    "\n",
    "In other words: on the day when most ventilators are needed, how many will be needed? For this tutorial, I'll pretend that we're making the prediction at the end of April -- I'll only use information that we could have had at that time.\n",
    "\n",
    "Background:\n",
    "\n",
    "- El Paso is a county in Texas (population 850,000) that is dealing with the impacts of COVID-19.\n",
    "- The community prediction site [Metaculus](https://www.metaculus.com) partnered with administrators at Texas Tech University Health Sciences Center to predict on questions that will guide decision making there.\n",
    "- This question is particularly decision-relevant: it's crucial to have enough ventilators for the patients who need them.\n",
    "\n",
    "## Loading question data from the Metaculus crowd prediction platform\n",
    "\n",
    "Ergo can load questions and make predictions on Metaculus and [Foretold](https://www.foretold.io/), another community prediction site.\n",
    "\n",
    "I'll load [the relevant question](https://pandemic.metaculus.com/questions/4204)* from Metaculus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "deWY7XbC_lfL",
    "outputId": "8d9edc62-656f-4057-86f3-68de80d9ecba"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MetaculusQuestion name=\"# ventilators needed\">"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metaculus = ergo.Metaculus(username=\"oughtpublic\", password=\"123456\", api_domain=\"pandemic\")\n",
    "ventilators_question = metaculus.get_question(4201, name=\"# ventilators needed\")\n",
    "ventilators_question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YBovzS0u_lfb"
   },
   "source": [
    "\\**Note: We're not asking exactly the same question as the Metaculus question. Most importantly, the Metaculus question is asking for the number of ventilators needed on a \"peak hospitalizations\" day that's defined in a complex way. To make things simpler, \n",
    "we're just asking how many ventilators are needed on the day when the most ventilators are needed.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Z3W5wZ5D_lfd"
   },
   "source": [
    "# A guess"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BrjTduwx_lfh"
   },
   "source": [
    "I'll start by making an uninformed guess. I'll do this before I look at any data or anyone else's predictions. That way, I can look back to this guess to see what I learn as I go through the forecasting process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "C5Deki8f_lfj"
   },
   "source": [
    "What is my 90% confidence interval for the number of ventilators needed? I think there is a \n",
    "\n",
    "- less than 5% chance that <3 people will require ventilation\n",
    "- less than 5% chance that >100 people will require ventilation\n",
    "\n",
    "So I'll go with a 90% confidence interval of [3, 100].\n",
    "\n",
    "I don't know much about El Paso, ICUs, or ventilators. I feel pretty uncertain and assign non-negligible probability to higher values. I'll go with a [lognormal distribution](https://en.wikipedia.org/wiki/Log-normal_distribution), which will assign more probability to the \"long tail\" of higher values than would a normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WsCM7v04_lfl"
   },
   "source": [
    "## Distributions in Ergo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EbqP_Wg8_lfo"
   },
   "source": [
    "In Ergo, I can generate a single sample from this distribution like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "mPYdonj4_lfr",
    "outputId": "ad742ccd-a55b-40c6-95fd-56ddc974c0ed"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray(20.191326, dtype=float32)"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ergo.lognormal_from_interval(3, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YlZM5dHC_lf6"
   },
   "source": [
    "To get many samples, I use `ergo.run`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 468,
     "referenced_widgets": [
      "ed07003e796340ea95df6b077b6f3c52",
      "8f8a3bff59bc48f8aae02690479e0a4e",
      "79a172d5df9a482a9d789152bfdef68a",
      "a523d676d5804446aa43c5b00676cbb1",
      "9b33393f2f294e20950807d25558e53a",
      "f5b0da939a984282ac3e7752317b0c77",
      "ef7c4f2fb0c449e0bfd943f4ba7f2578",
      "6d04c02b7af14703a5db48f35e2cb7cb"
     ]
    },
    "colab_type": "code",
    "id": "C0qda3fx_lf8",
    "outputId": "554c059b-9dad-4954-c7b5-4f3194ead3fd"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ed07003e796340ea95df6b077b6f3c52",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>output</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>91.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>82.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>49.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>14.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>10.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>6.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>7.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>24.71</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     output\n",
       "0     91.75\n",
       "1      4.04\n",
       "2     21.08\n",
       "3     82.26\n",
       "4     49.40\n",
       "..      ...\n",
       "995   14.95\n",
       "996   10.95\n",
       "997    6.60\n",
       "998    7.30\n",
       "999   24.71\n",
       "\n",
       "[1000 rows x 1 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def ventilators_needed():\n",
    "    \"# ventilators needed\"\n",
    "    return ergo.lognormal_from_interval(3, 100)\n",
    "\n",
    "samples = ergo.run(ventilators_needed, num_samples=1000)\n",
    "\n",
    "samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "svV7I1y__lgH"
   },
   "source": [
    "Why sample instead of manipulating distributions directly? To use distributions in our prediction, we need to be able to combine distributions for sub-predictions together. Combining distributions can be difficult, as it requires non-trivial math. \n",
    "\n",
    "Ergo allows you to create samplers (like the `ergo.lognormal_from_interval` above), which you can compose together using regular python operators (`*, +, -`). This allows you to focus on how you're modeling the problem, rather than the math. I'll build a complex model for this problem by composising samplers together."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9fl0PZSy_lgJ"
   },
   "source": [
    "## Visualizing distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vFGU8uMM_lgM"
   },
   "source": [
    "I can visualize these samples using my question's `show_prediction` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 473
    },
    "colab_type": "code",
    "id": "cJ6JO4i3_lgN",
    "outputId": "41cefe65-4446-4140-b4fb-b836b787ee91"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ventilators_question.show_prediction(samples[\"output\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mD8fIcJH_lgX"
   },
   "source": [
    "# Model V1: My guess"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Q-oHKZ9-_lgZ"
   },
   "source": [
    "I'll wrap my guess in a `Model` class so that I can more easily build on it step by step by inheriting from the class, adding more methods, and replacing methods with better implementations. This also lets me see how my prediction changes as I make it more sophisticated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5dZYOd4W_lgb"
   },
   "outputs": [],
   "source": [
    "class ModelV1:\n",
    "    \n",
    "    def ventilators_needed(self):\n",
    "        \"# ventilators needed\"\n",
    "        return ergo.lognormal_from_interval(3, 100)\n",
    "\n",
    "    def run(self):\n",
    "        samples = ergo.run(self.ventilators_needed, num_samples=1000)[\"output\"]\n",
    "        ventilators_question.show_prediction(samples); plt.show()\n",
    "        print(f\"Median estimate of # ventilators needed: {summarize_samples(samples)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YhvWnUHl_lgs"
   },
   "source": [
    "This doesn't change the result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 539,
     "referenced_widgets": [
      "cc3a953438ba4544b0b7629ea9be51e4",
      "98fe7a9301774a35a9dbaaf1402bfb78",
      "20366d0829d94ef5b297cc9e36aa4a02",
      "92be7593985f445caf877cf41a4fe409",
      "a10d992bcb654adfabbdcedf397d41cf",
      "45e7289f736e47838d67022faca30904",
      "51921cf33d84418f882ea72e4ebe5121",
      "97ce4a938f5b45b9a6ae68c12a6dad9a"
     ]
    },
    "colab_type": "code",
    "id": "ngO4ucxE_lgu",
    "outputId": "294d8cdb-45a4-4946-fbf4-f9060479e923"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cc3a953438ba4544b0b7629ea9be51e4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate of # ventilators needed: 16.87 (2.91 to 102.11)\n"
     ]
    }
   ],
   "source": [
    "model_v1 = ModelV1()\n",
    "model_v1.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "P0-o27kB_lg5"
   },
   "source": [
    "It's still an uninformed guess."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "r3PL0Tle_lg6"
   },
   "source": [
    "# Model V2: Decompose ventilators needed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vZcpylxA_lg9"
   },
   "source": [
    "## My decomposition\n",
    "\n",
    "My strategy for this question will be to break it into pieces and then improve my estimate for each piece.\n",
    "\n",
    "To estimate the maximum number of ventilators needed, I'll multiply the answers to:\n",
    "\n",
    "1. What's the maximum number of patients who will be in the ICU at once?\n",
    "2. What fraction of those patients will be on ventilators?\n",
    "\n",
    "So my decomposition looks like this:\n",
    "\n",
    "- **\\# ventilators needed** =\n",
    "  - max # icu patients *\n",
    "  - % of icu patients ventilated\n",
    " \n",
    "For both of these I'll make pretty uninformed guesses for now:\n",
    "\n",
    "1. I guess that about 5 to 200 people will be the maximum number of people in the ICU (but I have no idea)\n",
    "2. I'd guess that 1 out of 3 will need ventilators (another uninformed guess)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XEaymQ7SBEa6"
   },
   "source": [
    "### ICU cases\n",
    "\n",
    "I'll use the same `lognormal_from_interval` function I used above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "fadd112da92d4774a5ce8a751658411d",
      "cbd41a4b678f49ab95b96c8efa926525",
      "2636ef33454f40eea4fd888e4299ba94",
      "3af25ebaa81e43f5a4289a3ea39f043f",
      "f0e72289d8ae489ca16812dbe223480c",
      "36711bda08044d47a2dab76183d4e7c7",
      "124b26c1b95e4de589fffcda9942bacf",
      "7f41a64478c343a383c373a23f02aff7"
     ]
    },
    "colab_type": "code",
    "id": "ibvyiwYa_lg_",
    "outputId": "4f557db5-d8c1-4800-cec4-60f9127f107e"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fadd112da92d4774a5ce8a751658411d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median max # icu patients: 35.34 (5.51 to 188.67)\n"
     ]
    }
   ],
   "source": [
    "def max_icu_patients():\n",
    "    \"max # icu patients\"\n",
    "    return ergo.lognormal_from_interval(5, 200)\n",
    "\n",
    "show_marginal(max_icu_patients)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UH20C2Ca_lhJ"
   },
   "source": [
    "### Proportion of ICU patients on ventilators\n",
    "\n",
    "I'll use a beta-binomial distribution via `ergo.beta_from_hits`.\n",
    "\n",
    "`ergo.beta_from_hits`:\n",
    "1. Assumes that there's some constant underlying probability that a condition is met in a situation (in this case, the condition is that a patient will be on a ventilator given that they're in the ICU)\n",
    "2. Takes in a number of observations of the situation (patients in the ICU) and the number of observations that met the condition (number of patients in the ICU who needed a ventilator)\n",
    "3. Returns a sample from the beta-binomial distribution of underlying probabilities that the condition is met in the situation (again, the probability that a patient will be on a ventilator given that they're in the ICU)\n",
    "\n",
    "[This explanation](http://varianceexplained.org/statistics/beta_distribution_and_baseball/) helped me understand it.\n",
    "\n",
    "Here, I'll say that there were 3 patients in the ICU and 1 of them was ventilated.\n",
    "\n",
    "So, I think that about 1/3 of patients in the ICU are ventilated, but since I only have 3 total observations, I'm not at all confident and the true proportion could be much higher or lower."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "WX1DtGQt_lhM"
   },
   "outputs": [],
   "source": [
    "def frac_icu_ventilated():\n",
    "    \"% of icu patients ventilated\"\n",
    "    return ergo.beta_from_hits(1, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LhZGLXl0_lhY"
   },
   "source": [
    "This distribution looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "5897cb3999574e55882208c32aeeb46e",
      "8487d48a27e4462b8166efe3298af78a",
      "fb4f55c51f48400081686e466c0c3bdb",
      "d07e16caac50462b8606f04512454190",
      "47bb34d8e7d34c559e36a53b7c5f7189",
      "f6bc2484e3cd4cd3943c04b81748927e",
      "a8b262b451704da7a3b129a4b566a073",
      "d8ab0676571a430c9e7f8f5ee0316b11"
     ]
    },
    "colab_type": "code",
    "id": "HihFwg1S_lhZ",
    "outputId": "00f64b5e-fc07-42f3-9fd7-22aa7d602f32"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5897cb3999574e55882208c32aeeb46e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median % of icu patients ventilated: 0.37 (0.09 to 0.75)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(frac_icu_ventilated)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "y0RDyd0g_lhm"
   },
   "source": [
    "## My new model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "s72JaOox_lho"
   },
   "source": [
    "My model now looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fyi-6Hfd_lhp"
   },
   "outputs": [],
   "source": [
    "class ModelV2(ModelV1):\n",
    "    \n",
    "    def ventilators_needed(self):\n",
    "        \"# ventilators needed\"\n",
    "        return self.frac_icu_ventilated() * self.max_icu_patients()   \n",
    "    \n",
    "    def max_icu_patients(self):\n",
    "        \"max # of icu patients\"\n",
    "        return ergo.lognormal_from_interval(5, 200)\n",
    "\n",
    "    def frac_icu_ventilated(self):\n",
    "        \"% of icu patients ventilated\"\n",
    "        return ergo.beta_from_hits(1, 3)\n",
    "    \n",
    "    def run(self):\n",
    "        # we want to be able to compare versions of the model as we change it, so we use some python \n",
    "        # metaprogramming to compute the prediction from our previous model.\n",
    "        prev_model_samples = ergo.run(self.__class__.__bases__[0]().ventilators_needed, num_samples=1000)[\"output\"]\n",
    "        \n",
    "        # we then plot them against one another, showing how the model has changed\n",
    "        this_model_samples = ergo.run(self.ventilators_needed, num_samples=1000)[\"output\"]\n",
    "        samples_df = pd.DataFrame(data={\"Previous model\": prev_model_samples, \"This model\": this_model_samples})\n",
    "        ventilators_question.show_prediction(samples_df); plt.show()\n",
    "        print(f\"Median estimate of # ventilators needed: {summarize_samples(this_model_samples)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 588,
     "referenced_widgets": [
      "4ebbc2d79e5d47f2a40865eed5afcc44",
      "8210d3fc84af41f18e5ed0b0caf37567",
      "881b77e97cd44454a106ea2dede732fd",
      "ad743d3c4f174492afb1146658452e48",
      "44b233000ff445a5adc95642849a6b03",
      "d9159cf9d8364dcf94f88e1282c477e4",
      "cb8e5668121f48e195c327b25141bbd8",
      "f4eb4b40622e4d6781d73da36487051a",
      "e3a6e10be27543fba3bbcef23241867e",
      "a42d763defad44338303ac2891ec75a2",
      "0419231afc1a45b8b396d1228c7df770",
      "491a883cc82b432497cee1195cb8308e",
      "b29be259beca48579dbafce68f0e52fa",
      "e28863ead98a42888cf461008373d052",
      "f8bd3bef641d48839fd1de99f6bffcd8",
      "ee0e19dc85924cdbb757442bf61e2d07"
     ]
    },
    "colab_type": "code",
    "id": "IQD55Oz0_lh5",
    "outputId": "f788a6ab-3614-4072-f2c3-b8438855d0ab"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4ebbc2d79e5d47f2a40865eed5afcc44",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e3a6e10be27543fba3bbcef23241867e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate of # ventilators needed: 11.04 (1.20 to 90.88)\n"
     ]
    }
   ],
   "source": [
    "model_v2 = ModelV2()\n",
    "model_v2.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dBs1HY6b_liE"
   },
   "source": [
    "This model's prediction is about the same as the previous model's."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UYDTZ9VV_liF"
   },
   "source": [
    "# Model V3: Use external model for # of ICU patients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8dk4FUqH_liI"
   },
   "source": [
    "So far, I've just made an uninformed guess about the maximum number of patients in the ICU.\n",
    "\n",
    "I could do more modeling myself to get a more accurate number, but it seems better to just use [this model](https://github.com/shaman-lab/COVID-19Projection)\n",
    " ([paper](https://www.medrxiv.org/content/10.1101/2020.03.21.20040303v2)) from the Shaman lab at Columbia university.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kLBrJ2eX_liK"
   },
   "source": [
    "\\**Note: the Columbia model directly makes predictions for how many ventilators will be needed, so it would be most sensible to just use those numbers directly. But, that wouldn't make for a very useful or informative tutorial. So instead, I'll pretend that the ventilator predictions don't exist, and I'll make my own based on the Columbia prediction for number of people in the ICU.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_76QDAE3_liM"
   },
   "source": [
    "Our team made an interface to the Columbia projections, which I'll use here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "iYq8esog_liN"
   },
   "outputs": [],
   "source": [
    "from ergo.contrib.el_paso import shaman\n",
    "\n",
    "cu_projections = shaman.load_cu_projections(\"El Paso County TX\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HfxPuIaG_liW"
   },
   "source": [
    "## My new model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KcI5qdTa_liY"
   },
   "source": [
    "Now I can change my model to use the Columbia projections rather than my guess from before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 588,
     "referenced_widgets": [
      "7b83ffdb4f4d49c99b946f365c315309",
      "9d9d105fd45d4fb5a20f40e7a9035a8e",
      "085cfb729b2348d8bae06a8123e860ac",
      "9125fdf4b6214a7b887edb72450a3b47",
      "69d2c3d8039d43b2a85e74d2e2653b31",
      "53160cb4083a4754bbdd17015eaef197",
      "80ccbce1bce441b69ee5c04d12629aeb",
      "6444dc52389e433ab9acaada734b6008",
      "6962f3b2fb0940dda44b56d51f535734",
      "c0bcb4e692e14de5b9b7d50a272fc34d",
      "7688cba09dc14fbb8a65c27ec23a4326",
      "3986810056d5481b925c9d50cc502f0e",
      "86a62fcae307430596fdb4c6cea0bf74",
      "b84783d1b7954b1588c46fe963eeb51d",
      "e836388591c84d42a5ddc92f66e775a4",
      "8892834c1c484966b351a73f9c637547"
     ]
    },
    "colab_type": "code",
    "id": "DYZfBC8D_liZ",
    "outputId": "c41fd27e-7d27-4bef-91ed-c88f54ca493c"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7b83ffdb4f4d49c99b946f365c315309",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6962f3b2fb0940dda44b56d51f535734",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate of # ventilators needed: 35.31 (5.19 to 489.98)\n"
     ]
    }
   ],
   "source": [
    "class ModelV3(ModelV2):\n",
    "    def max_icu_patients(self):\n",
    "        \"max # of icu patients\"\n",
    "        return max(shaman.cu_projections_for_dates(\"ICU\", date(2020,5,1), date(2020,6,1), cu_projections))\n",
    "\n",
    "model_v3 = ModelV3()\n",
    "model_v3.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SCGmxIBW_lik"
   },
   "source": [
    "### Why did my model results change?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NsaB3ukY_lip"
   },
   "source": [
    "My new model projects many more ventilators needed. I can see that this is because the Columbia model has a much fatter tail for the max number of ICU patients than my previous guess had:\n",
    "\n",
    "#### 1. My previous guess for max ICU patients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "9794b340e011442e82c2fbf06082542f",
      "4270a823d7d547c6a237cfe036f574fc",
      "f470fe54cdc84e3a82d7a4d91d778e47",
      "7b5c93e0f38140cd91f105b2f78d343b",
      "617e93e32fe3446d9d8ae42f7a327424",
      "d2fdeacbbfd14a6e804bfbff76a163d1",
      "a40148ebedb14ee7a582072541e5f796",
      "ecbe7f0c6c1742bc8fe0073efbdaf31c"
     ]
    },
    "colab_type": "code",
    "id": "lT0AAMuT_lir",
    "outputId": "d216dcc4-af09-4c1a-eea7-0d99f6d4718b"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9794b340e011442e82c2fbf06082542f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median max # of icu patients: 32.52 (4.56 to 224.81)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(model_v2.max_icu_patients)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hLAWCmYw_li3"
   },
   "source": [
    "#### 2. The Columbia model prediction for max ICU patients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "84cdaae78940476e8b1324fb8e690746",
      "a81a0eece2134675a02fdd9048ce1b15",
      "d3b550f58ab842d2a7e853495cc9507f",
      "87b9e93fa1bb436695ef397d2a82efd1",
      "096b1ef71fe443299525194770586a41",
      "5249cf4e6f954a70aefa5cd2d8f38535",
      "88dc2c3b05dc431f92cc80f581d5e805",
      "97dd3c82728b481bbd60eaf8e1b8bb23"
     ]
    },
    "colab_type": "code",
    "id": "HUmicq7b_li5",
    "outputId": "4882ae8b-c062-4e9c-c54f-add41184e90a"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "84cdaae78940476e8b1324fb8e690746",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median max # of icu patients: 106.00 (21.00 to 1174.00)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(model_v3.max_icu_patients)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mF6-yghq_ljI"
   },
   "source": [
    "# Model V4: Decompose fraction of ICU patients ventilated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OG98mFD2_ljL"
   },
   "source": [
    "I want to improve my estimate for the fraction of ICU patients ventilated:\n",
    "\n",
    "- \\# ventilators needed =\n",
    "  - max # icu patients *\n",
    "  - **% of icu patients ventilated**\n",
    "  \n",
    "I can break it down as:\n",
    "- **% of icu patients ventilated** =\n",
    "  - \\% icu patients that need ventilation at some point while in the ICU *\n",
    "  - icu-ventilation adjustment (see below)\n",
    "  \n",
    "I'll skip guessing these values and just go ahead and use data to model them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "o5xVJiyV_ljO"
   },
   "source": [
    "## Fraction of ICU patients that need ventilation at some point during their ICU stay\n",
    "\n",
    "I'll model this based on the data that [PabloStafforini et al gathered on Metaculus](https://pandemic.metaculus.com/questions/4154/#comment-28155)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 173
    },
    "colab_type": "code",
    "id": "lWOXFS-b_ljP",
    "outputId": "1bd131be-78d5-4aa4-99c3-f592792960de"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>study</th>\n",
       "      <th>source_url</th>\n",
       "      <th>icu</th>\n",
       "      <th>ventilated</th>\n",
       "      <th>%_ventilated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Wuhan 1</td>\n",
       "      <td>https://www.thelancet.com/pdfs/journals/lanres...</td>\n",
       "      <td>52</td>\n",
       "      <td>22</td>\n",
       "      <td>0.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Wuhan 2</td>\n",
       "      <td>http://doi.org/10.1001/jama.2020.1585</td>\n",
       "      <td>36</td>\n",
       "      <td>17</td>\n",
       "      <td>0.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Lombardy</td>\n",
       "      <td>http://doi.org/10.1001/jama.2020.5394</td>\n",
       "      <td>1300</td>\n",
       "      <td>1150</td>\n",
       "      <td>0.88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>UK</td>\n",
       "      <td>https://doi.org/10.1136/bmj.m1201</td>\n",
       "      <td>196</td>\n",
       "      <td>132</td>\n",
       "      <td>0.67</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      study  ... %_ventilated\n",
       "0   Wuhan 1  ...         0.42\n",
       "1   Wuhan 2  ...         0.47\n",
       "2  Lombardy  ...         0.88\n",
       "3        UK  ...         0.67\n",
       "\n",
       "[4 rows x 5 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ventilated_data = [\n",
    "    {\n",
    "        \"study\": \"Wuhan 1\",\n",
    "        \"source_url\": \"https://www.thelancet.com/pdfs/journals/lanres/PIIS2213-2600(20)30110-7.pdf\",\n",
    "        \"icu\": 52,\n",
    "        \"ventilated\": 22\n",
    "    },\n",
    "    {\n",
    "        \"study\": \"Wuhan 2\",\n",
    "        \"source_url\": \"http://doi.org/10.1001/jama.2020.1585\",\n",
    "        \"icu\": 36,\n",
    "        \"ventilated\": 17\n",
    "    },\n",
    "    {\n",
    "        \"study\": \"Lombardy\",\n",
    "        \"source_url\": \"http://doi.org/10.1001/jama.2020.5394\",\n",
    "        \"icu\": 1300,\n",
    "        \"ventilated\": 1150\n",
    "    },\n",
    "    {\n",
    "        \"study\": \"UK\",\n",
    "        \"source_url\": \"https://doi.org/10.1136/bmj.m1201\",\n",
    "        \"icu\": 196,\n",
    "        \"ventilated\": 132\n",
    "    },\n",
    "]\n",
    "\n",
    "ventilated_df = pd.DataFrame(ventilated_data)\n",
    "\n",
    "ventilated_df[\"%_ventilated\"] = ventilated_df[\"ventilated\"] / ventilated_df[\"icu\"]\n",
    "\n",
    "ventilated_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7CMXGy4O_ljZ"
   },
   "source": [
    "I'll use `ergo.beta_from_hits` again to model the fraction of ICU patients that we expect to need ventilation.\n",
    "\n",
    "Naively, we'd just add up all of the ICU patients across all of the studies and all of the ventilated patients across all of the studies and input them to `ergo.beta_from_hits`.\n",
    "\n",
    "However, recall from above that `ergo.beta_from_hits` assumes that all of the samples provided to it are from the same situation.\n",
    "\n",
    "In reality, the situation differs between the 4 studies and between the studies and El Paso, due to differences in how COVID works in different locations, differences in measurement and record-keeping, etc.\n",
    "\n",
    "So if we just added up the ICU and ventilated patients and input them into `ergo.beta_from_hits`, we'd be way too confident in our answer.\n",
    "\n",
    "Instead, I'll do a bit of somewhat-unprincipled math to:\n",
    "1. Gain some uncertainty\n",
    "2. Instead of weighing every study participant equally (and thus weighing large studies overwhelmingly more than small studies), weigh larger studies somewhat more"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 173
    },
    "colab_type": "code",
    "id": "9-3bmB7m_lja",
    "outputId": "0dbf05cf-8f52-4d20-91ac-52e43fd0e9a7"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>study</th>\n",
       "      <th>source_url</th>\n",
       "      <th>icu</th>\n",
       "      <th>ventilated</th>\n",
       "      <th>%_ventilated</th>\n",
       "      <th>log_participants</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Wuhan 1</td>\n",
       "      <td>https://www.thelancet.com/pdfs/journals/lanres...</td>\n",
       "      <td>52</td>\n",
       "      <td>22</td>\n",
       "      <td>0.42</td>\n",
       "      <td>3.95</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Wuhan 2</td>\n",
       "      <td>http://doi.org/10.1001/jama.2020.1585</td>\n",
       "      <td>36</td>\n",
       "      <td>17</td>\n",
       "      <td>0.47</td>\n",
       "      <td>3.58</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Lombardy</td>\n",
       "      <td>http://doi.org/10.1001/jama.2020.5394</td>\n",
       "      <td>1300</td>\n",
       "      <td>1150</td>\n",
       "      <td>0.88</td>\n",
       "      <td>7.17</td>\n",
       "      <td>0.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>UK</td>\n",
       "      <td>https://doi.org/10.1136/bmj.m1201</td>\n",
       "      <td>196</td>\n",
       "      <td>132</td>\n",
       "      <td>0.67</td>\n",
       "      <td>5.28</td>\n",
       "      <td>0.26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      study  ... weight\n",
       "0   Wuhan 1  ...   0.20\n",
       "1   Wuhan 2  ...   0.18\n",
       "2  Lombardy  ...   0.36\n",
       "3        UK  ...   0.26\n",
       "\n",
       "[4 rows x 7 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ventilated_df[\"log_participants\"] = np.log(ventilated_df[\"icu\"])\n",
    "ventilated_df[\"weight\"] = ventilated_df[\"log_participants\"] / sum(ventilated_df[\"log_participants\"])\n",
    "ventilated_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "kUfv-PiN_ljm",
    "outputId": "ced5dfdf-faba-434d-9370-602c5c34412a"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6636313917323585"
      ]
     },
     "execution_count": 22,
     "metadata": {
      "tags": []
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "weighted_avg_percent_ventilated = sum(ventilated_df[\"%_ventilated\"] * ventilated_df[\"weight\"])\n",
    "weighted_avg_percent_ventilated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0khunggV_ljw"
   },
   "outputs": [],
   "source": [
    "def icu_receive_ventilation():\n",
    "    \"% icu patients that need ventilation at some point while in the ICU\"\n",
    "    # as explained above, this sets our level of uncertainty\n",
    "    total_participants = 200\n",
    "    return ergo.beta_from_hits(total_participants * weighted_avg_percent_ventilated, total_participants)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gKjLeSuO_lj6"
   },
   "source": [
    "## ICU-ventilation adjustment\n",
    "\n",
    "### Why is this necessary?\n",
    "\n",
    "It might seem that I could just multiply `(max # icu patients) * (% icu patients that need ventilation at some point while in the ICU)` to get `ventilators needed`, but I cannot.\n",
    "\n",
    "To see this, first imagine that:\n",
    "1. There are 100 patients in the ICU\n",
    "2. 1/2 of ICU patients need ventilation at some point during their stay\n",
    "\n",
    "Then `(max # icu patients) * (% icu patients that need ventilation at some point while in the ICU)` = 50. This may give too high an estimate of ventilators needed. \n",
    "\n",
    "Imagine that:\n",
    "1. Patients who will need ventilation at some point during their ICU stay remain in the ICU for the same total amount of time as ICU patients who will never need ventilation\n",
    "2. ICU patients only need ventilation for 1/2 of their ICU stay\n",
    "\n",
    "In this scenario, in fact only 1/4 * 100 = 25 ICU patients will need ventilation at any one time.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "znMqOFQm_lj8"
   },
   "source": [
    "\\**Note: Alternatively, `(max # icu patients) * (% icu patients that need ventilation at some point while in the ICU)` may give an underestimate. Imagine that:*\n",
    "1. *Patients who will need ventilation at some point during their ICU stay remain in the ICU 10 times as long as ICU patients who will not never need ventilation*\n",
    "2. *All ICU patients who need ventilation need it for their entire stay*\n",
    "\n",
    "*The math is a bit more complicated and I haven't done it, but hopefully it's clear that in this scenario, almost all 100 of the patients will need ventilation at any given time.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ac8wF4pW_lj-"
   },
   "source": [
    "### Making the adjustment\n",
    "\n",
    "My model needs some way to adjust for this complication. My guess is that this parameter won't actually have a huge impact, so I'll just guess that it's fairly close to 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8tavm2ej_lkG"
   },
   "outputs": [],
   "source": [
    "def icu_ventilation_adjustment(self):\n",
    "    return ergo.lognormal_from_interval(0.5, 1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XxrENo1Z_lkO"
   },
   "source": [
    "## My new model\n",
    "\n",
    "### New decomposition\n",
    "My new overall decomposition is:\n",
    "- \\# ventilators needed =\n",
    "  - max # icu patients *\n",
    "  - % of icu patients ventilated\n",
    "      - \\% icu patients that need ventilation at some point while in the ICU *\n",
    "      - icu-ventilation adjustment\n",
    "\n",
    "Updating my model with the new decomposition and submodels:"
   ]
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate of # ventilators needed: 58.87 (11.50 to 740.66)\n"
     ]
    }
   ],
   "source": [
    "class ModelV4(ModelV3):\n",
    "    def icu_receive_ventilation(self):\n",
    "        \"% icu patients that need ventilation at some point while in the ICU\"\n",
    "        # as explained above, this sets our level of uncertainty\n",
    "        total_participants = 200\n",
    "        return ergo.beta_from_hits(total_participants * weighted_avg_percent_ventilated, total_participants)\n",
    "    \n",
    "    def icu_ventilation_adjustment(self):\n",
    "        \"adjustment to the % of icu patients ventilated at some point to get the % currently ventilated\"\n",
    "        return ergo.lognormal_from_interval(0.5, 1.5)\n",
    "        \n",
    "    def frac_icu_ventilated(self):\n",
    "        \"% of icu patients ventilated\"\n",
    "        return self.icu_receive_ventilation() * self.icu_ventilation_adjustment()\n",
    "\n",
    "model_v4 = ModelV4()\n",
    "model_v4.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5-meU51l_lkb"
   },
   "source": [
    "This doesn't change my prediction that much."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Gtzx82tN_lkd"
   },
   "source": [
    "# Model V5: Ensemble with community prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_b1q0xVW_lke"
   },
   "source": [
    "In the previous model, I used a model based on data to predict the proportion of ICU patients that need ventilation at some point during their ICU stay.\n",
    "\n",
    "However, there's a Metaculus question for [what proportion of hospital patients will be admitted to the ICU](https://pandemic.metaculus.com/questions/4155/what-portion-of-in-hospital-cases-in-el-paso-county-will-require-admission-to-the-icu/), and another one for [what proportion of hospital patients will require ventilation](https://pandemic.metaculus.com/questions/4154/what-portion-of-in-hospital-patients-with-covid-19-in-el-paso-county-will-require-invasive-ventilation/).\n",
    "\n",
    "If I assume that all ventilated patients are in the ICU, I can do some simple math to get a Metaculus estimate for proportion of ICU patients ventilated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "O41vyovK_lkg"
   },
   "outputs": [],
   "source": [
    "icu_admit_per_hospital_admit_question = metaculus.get_question(4155)\n",
    "ventilation_per_hospital_admit = metaculus.get_question(4154)\n",
    "\n",
    "def metaculus_icu_receive_ventilation():\n",
    "    \"\"\"\n",
    "    The Metaculus community's implicit prediction for \n",
    "    % icu patients that need ventilation at some point while in the ICU\n",
    "    \"\"\"\n",
    "    icu_admit_per_hospital_admit_sample = icu_admit_per_hospital_admit_question.sample_community()\n",
    "    ventilation_per_hospital_admit_sample = ventilation_per_hospital_admit.sample_community()\n",
    "    \n",
    "    # each of these should be a positive number,\n",
    "    # but we're sampling from a distribution that includes 0\n",
    "    # and negative numbers. So clip them at just above 0.\n",
    "    icu_clipped = max(icu_admit_per_hospital_admit_sample, 0.01)\n",
    "    ventilated_clipped = max(ventilation_per_hospital_admit_sample, 0.01)\n",
    "    \n",
    "    return ventilated_clipped / icu_clipped"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KLpGiSLL_lko"
   },
   "source": [
    "Comparing to my model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 330,
     "referenced_widgets": [
      "fba3ec02aa4a428a98ea63c96e611d6f",
      "d61c34f223884679b6f0623ebff822d6",
      "25fa34aee0684f7da9aab7b056f26520",
      "2f1c5559cd1b4977b61edb5cb5fec4f7",
      "1c356661f77e46ff8b988d94ee1c129b",
      "3be321ba35654e3da7f909d912a5eb2d",
      "96ddff2541ff4dbdbdbc060ee708503f",
      "9d92832595cc4197a1af3e1a848905cf"
     ]
    },
    "colab_type": "code",
    "id": "M0txAQyJ_lkq",
    "outputId": "16f0282f-e514-407e-a8ac-02276de2ae05"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fba3ec02aa4a428a98ea63c96e611d6f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_samples = 100\n",
    "metaculus_samples = [metaculus_icu_receive_ventilation() for _ in range(num_samples)]\n",
    "seaborn.distplot(metaculus_samples)\n",
    "\n",
    "model_samples = ergo.run(model_v4.icu_receive_ventilation, num_samples=num_samples)\n",
    "seaborn.distplot(model_samples).set_title(model_v4.icu_receive_ventilation.__doc__)\n",
    "plt.legend(labels=[\"Metaculus\", \"My model\"])\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dQOCeY-s_lk1"
   },
   "source": [
    "The implicit community prediction is similar to my model prediction, but much less confident.\n",
    "\n",
    "## My new model - now with ensembling!\n",
    "I can combine my prediction and the community prediction into an ensembled prediction. I'll sample from the Metaculus community prediction half the time, and from my model half the time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 588,
     "referenced_widgets": [
      "2f47906f78d24e12916d03e77930586d",
      "92e5a87155f1461d87d2a8b83fe420bd",
      "726e2200db2e43308b8b94353393d6d4",
      "3ff74b00be364c64bde59bf00a91433c",
      "f7f1fbecca4c4b90a4984bd572eb70f0",
      "4e26bb807bd044569691d807a738cb54",
      "d798e834176047d38f851628c627fd84",
      "595c237ccee74a47b0dcf839ac3eb09e",
      "ad2f907c105b416380611e1e3aee87cf",
      "4f527d4cdd324032b14cb305e30bb832",
      "5548be5085674a658895432c3e95e54a",
      "ad24ccfa718f44d5943bf158578e9cbb",
      "e841344869d44b08ad00eab27a57239a",
      "609e049523eb42f7b48f48adb49c7b1d",
      "c4b3dbe165f948f4b0d8550dcd165a1b",
      "16fd2ded040a4ef19a63d9a1e4d760ce"
     ]
    },
    "colab_type": "code",
    "id": "QUKFLE5f_lk3",
    "outputId": "56e8b5d2-f94f-4e62-ef67-39b669013d82"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2f47906f78d24e12916d03e77930586d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ad2f907c105b416380611e1e3aee87cf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate of # ventilators needed: 44.82 (7.12 to 608.06)\n"
     ]
    }
   ],
   "source": [
    "class ModelV5(ModelV4):\n",
    "    def my_model_icu_receive_ventilation(self):\n",
    "        \"% icu patients that need ventilation at some point while in the ICU\"\n",
    "        ventilation_pseudocounts = 25 + 17 + 0.05 * 1150 + 0.1 * 132\n",
    "        icu_pseudocounts = 100 + 36 + 0.05 * 1300 + 0.1 * 196\n",
    "        return ergo.beta_from_hits(ventilation_pseudocounts, icu_pseudocounts)\n",
    "    \n",
    "    def metaculus_icu_receive_ventilation(self):\n",
    "        \"\"\"\n",
    "        The Metaculus community's implicit prediction for \n",
    "        % icu patients that need ventilation at some point while in the ICU\n",
    "        \"\"\"\n",
    "        icu_admit_per_hospital_admit_sample = icu_admit_per_hospital_admit_question.sample_community()\n",
    "        ventilation_per_hospital_admit_sample = ventilation_per_hospital_admit.sample_community()\n",
    "\n",
    "        icu_clipped = max(icu_admit_per_hospital_admit_sample, 0.01)\n",
    "        ventilated_clipped = max(ventilation_per_hospital_admit_sample, 0.01)\n",
    "\n",
    "        return ventilated_clipped / icu_clipped\n",
    "    \n",
    "    def icu_receive_ventilation(self):\n",
    "        \"% icu patients that need ventilation at some point while in the ICU\"\n",
    "        # use the community prediction half the time, my model half the time \n",
    "        if ergo.flip(0.5):\n",
    "            return self.metaculus_icu_receive_ventilation()\n",
    "        else:\n",
    "            return self.my_model_icu_receive_ventilation()\n",
    "\n",
    "model_v5 = ModelV5()\n",
    "model_v5.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "H4zmZ8ZCIaHr"
   },
   "source": [
    "Not a big change, though it is apparent that with the less-confident community prediction added in, the model is now less confident that El Paso will need so many ventilators."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sakd1zFN_lk_"
   },
   "source": [
    "### Marginals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DMObw1Db_llB"
   },
   "source": [
    "This is my last model, so let's also take a look at all the predictions for its marginals (the steps in the decomposition):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "91e786a51fae44aa845e23087346b7d1",
      "acf477b6d290417590568af05dad0cde",
      "0b7d85c0150d4e238c5d18b93fffcd05",
      "8b0f3318db2d4d11a41b70304356ecf9",
      "81c6ba6871bb42a7a9d264228d9317da",
      "f6e66b592002417ea7d38d098a0c0677",
      "a303203152ad44e78def77ff035b6f72",
      "58e732c7b0ab422a80fe9d79379adb32"
     ]
    },
    "colab_type": "code",
    "id": "cy3QPp3n_llG",
    "outputId": "cc884c59-9703-4e66-83fb-4a35ab9f1d70"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "91e786a51fae44aa845e23087346b7d1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median max # of icu patients: 106.50 (22.00 to 1174.00)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(model_v5.max_icu_patients)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "5d1ee885ae504045a22bff7925cbb0f8",
      "f310ab947b8d4a57b919363bab896815",
      "e0d00a5cc10b461cb73c7a384ec5281e",
      "e0dddeb9e3244cd2a52bf583e62a6f41",
      "bcf28638755a4dd0b50871a684410ef6",
      "b8c90dd3b48642c6bae38bbb7c6ecbe1",
      "aa35d5c8fc6f42ab85b1ffaa528b03f5",
      "42b5e29b2354455aa6eb09bdf3e6dd41"
     ]
    },
    "colab_type": "code",
    "id": "snYuGxES_llP",
    "outputId": "25571165-963a-4e91-84ad-7c7930c590f5"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5d1ee885ae504045a22bff7925cbb0f8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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H46iiF5FyM2Wid/efA90z2Pc5QIe7b3P3JHArcMkM9jMnBpOpCU/EAkfuPKWKXkTKzZT3jM3Rq83sSeBF4FPu/jSwDNgVWWc3sD5Px8ubmx/eCUBHZz9DyfSR1+Nlqv1DSvQiUmbykegfB1a5e7+ZvQX4MbBuujsxsw3ABoCVK1fmIazpSaac6vjEf+DUVccw0E3CRaTszHrUjbv3unt/+PwOIGFmrcAeYEVk1eVh20T7udHd2929va2tbbZhTVsynaZ6ghE3AFVmNNTE6eobmcOoRERmb9aJ3sxOMDMLn58T7vMg8CiwzszWmFk1cCmwabbHK5SpKnqA5to4+3uH5ygiEZH8mLLrxsxuAV4HtJrZbuDTQALA3W8A3gX8LzNLAUPApe7uQMrMrgLuAmLAxrDvviSNpscmregBmmoTdKqiF5EyM2Wid/fLplj+NeBrEyy7A7hjZqHNrZFUesqKvqk2zvaDg3MUkYhIfujK2NBoLl03dQkODoyQSo/NUVQiIrOnRA+kx5y0O4kpu27iuMOBfo28EZHyoUQPJFNBhV4z5cnYBIBOyIpIWVGiB5JhV8zUJ2ODUxpK9CJSTpToOVrRJ3Kt6DXyRkTKiBI9Ryv6qbpuGmriVBl0qaIXkTKiRE+kop+i6yZWZSxurGF/ryp6ESkfSvQcTfRTDa8EWNpcw/4+VfQiUj6U6Mn9ZCzA0qZaOlXRi0gZUaIHRqdR0S9prqFTFb2IlBElemAkPY1E31TLgf4ko7o6VkTKhBI9kYo+l66b5loADvSr+0ZEyoMSPUEfvQHxmE257tLmGgCNvBGRsqFETzDqJhGrosqmTvRLmoKKXlfHiki5UKInTPQ59M/D0Ype89KLSLlQoifoupnqqtiMxY01VBl0qqIXkTKhRE9Q0edyIhaCq2NbG2vUdSMiZWPK7GZmG82s08yemmD5e8xsi5n92sweMLPTI8u2h+1PmNnmfAaeT8n0GIkcTsRmLG2u1clYESkbuZSxNwEXTbL8BeC17v5K4LPAjeOWv97dz3D39pmFWHjJ1FhOY+gzljbXqI9eRMrGlNnN3X8OdE+y/AF3PxS+fAhYnqfY5sxoeozqeCzn9duaatVHLyJlI9999B8EfhJ57cBPzewxM9uQ52PlzUhqjOppdd3UcHAgeWQyNBGRUhbP147M7PUEif78SPP57r7HzJYAd5vZc+FfCNm23wBsAFi5cmW+wsrJ6LS7bo5eHXvSgrpChSUikhd5qejN7FXAN4FL3P1gpt3d94T/dgK3A+dMtA93v9Hd2929va2tLR9h5SyZzn3UDUSvjlX3jYiUvlknejNbCfwI+CN3/02kvcHMmjLPgQuBrCN3isndp30y9ujVsTohKyKlb8quGzO7BXgd0Gpmu4FPAwkAd78BuBZYDPxfC6YQSIUjbJYCt4dtceBmd7+zAO9hVlJjjpPbhGYZS8KKvkvTFYtIGZgy0bv7ZVMs/xDwoSzt24DTj9+itEzn7lIZixtqiFWZKnoRKQsVf2XsTBJ9cHVstfroRaQsKNGnc7sx+HhLm2t10ZSIlIW8Da8sV5mKPtdJzW5+eCcQDMncuq/vyOvL18/tkFARkVypos9U9NPougFoqk3QOzxaiJBERPJKiX4atxGMaqqLM5hMkxrT1bEiUtqU6NMzS/TNtQkA+odTeY9JRCSfKj7Rj85g1A1Ac21weqNXiV5ESlzFJ/qRGSb6prCi7x1SP72IlLaKT/SjM+y6aQor+r4RVfQiUtoqPtEnU2NUWXAR1HQ01MSpMuhTRS8iJa7iE/1IOpjQLJyTJ2dVZjTWxNVHLyIlr+IT/eg0bgw+XnNdgj6NpReRElfxiT6Znt4UxVFNtQn6VNGLSIlTop9NRV8b19WxIlLylOhTY9Oe/iCjqTa8Ojatq2NFpHQp0U/zNoJRmatjNcRSREqZEv00byMYlbloSkMsRaSU5ZThzGyjmXWaWdZ7vlrgH82sw8y2mNlZkWVXmNlvw8cV+Qo8X2ZT0TdpGgQRKQO5ZribgIsmWX4xsC58bAC+DmBmiwjuMbseOAf4tJktnGmwhTCbir65LqzodUJWREpYThnO3X8OdE+yyiXAdzzwELDAzE4E3gzc7e7d7n4IuJvJvzDm3OgshlfWV8eoMlX0IlLa8tVHvwzYFXm9O2ybqP04ZrbBzDab2eaurq48hTW59JgzmvYZd91UmYVj6VXRi0jpKpmTse5+o7u3u3t7W1vbnBxzaDQNTH/myqim2rgumhKRkpavRL8HWBF5vTxsm6i9JAwmgwQ9m0TfrFsKikiJy1ei3wS8Lxx9cy7Q4+57gbuAC81sYXgS9sKwrSQMJcOKfoZdNxBU9L1DquhFpHTFc1nJzG4BXge0mtlugpE0CQB3vwG4A3gL0AEMAh8Il3Wb2WeBR8NdXefuk53UnVMDI0GiT8wq0ScYGk0zkkpTE4/lKzQRkbzJKdG7+2VTLHfgygmWbQQ2Tj+0whsazUfXTfARdvaOsGJRfV7iEhHJp5I5GVsMg2HXTc1sEn04lr6zbzgvMYmI5FtFJ/r8dN0EFf3+3pG8xCQikm8Vnejz0XWTme+ms1cVvYiUpopO9Jmum9kk+vrqGDEz9vepoheR0lTZiX5k9sMrg6tj4+xXRS8iJaqyE30eKnoI+um7VNGLSImq7EQ/miJeZVSZzWo/TbUJVfQiUrIqOtEPJdOzruYBmuviGnUjIiWrohP9wEh6Vv3zGU21CXqGRhkOJ0kTESklFZ3oh0ZTM74xeFTm6lj104tIKaroRD+YTM/qqtiMzFh69dOLSCmq7EQ/kp7VVbEZujpWREpZZSf60VRe+uibazXfjYiUrspO9HkadVNfHSMRM1X0IlKSKjvRj+Qn0ZsZS5pqNd+NiJSkyk70yfx03QAsaa6hU6NuRKQEVWyid3eGRvNT0QO0NtZwoF+JXkRKT05ZzswuMrOtZtZhZldnWf5lM3sifPzGzA5HlqUjyzblM/jZGEmNMZp2avOU6NuaajSOXkRK0pS3EjSzGHA98HvAbuBRM9vk7s9k1nH3T0TW/whwZmQXQ+5+Rv5Czo/e4VEAahL5uc9ra2MN3YNJUukx4nnqDhIRyYdcMtI5QIe7b3P3JHArcMkk618G3JKP4Aqpbzi46UhtnhJ9W1MN7tA9kMzL/kRE8iWXRL8M2BV5vTtsO46ZrQLWAD+LNNea2WYze8jM3jHRQcxsQ7je5q6urhzCmp2jiT5PXTeN1QB0qZ9eREpMvvsYLgVuc/fo7F6r3L0duBz4ipmtzbahu9/o7u3u3t7W1pbnsI7XF3bd1MbzV9GD5rsRkdKTS6LfA6yIvF4etmVzKeO6bdx9T/jvNuA+ju2/L5p8d920NgaJ/kC/um5EpLTkkugfBdaZ2RozqyZI5seNnjGzlwELgQcjbQvNrCZ83gqcBzwzfttiOFLR56nrJpPoVdGLSKmZctSNu6fM7CrgLiAGbHT3p83sOmCzu2eS/qXAre7ukc1PBb5hZmMEXyqfj47WKaZ8V/QNNXHqq2MaSy8iJWfKRA/g7ncAd4xru3bc689k2e4B4JWziK9geodTmM3+frFRGksvIqWoYgd89w2P0lgdn/X9YqN0dayIlKIKTvSpI/PI50tboyp6ESk9FZzoR4/cGSpfWpuqVdGLSMmp4ESf34r+5od3srdnmEODo/zrgzu4+eGdedu3iMhsKNHnUWNNsL/+kVRe9ysiMhsVnOhHacxz101TTbC//mElehEpHRWc6AtQ0ddmKvrRvO5XRGQ2lOjzqCnsuulTRS8iJaQiE/3waJpkeozmPHfdHK3olehFpHRUZKLPVNz5rugTsSpq4lX0KdGLSAmp0EQf9KHnO9FDMPJGJ2NFpJRUaKIPK/qa/HbdQPDloa4bESkllZ3oC1TR62SsiJSSikz0meGP+Z4CAaCxNqHhlSJSUioy0fcWsKJvqo0zPDrGaHos7/sWEZmJikz0ma6VfA+vhKNj6XVCVkRKRYUm+qBrpbEAFX1LXfDlcXhI3TciUhpySvRmdpGZbTWzDjO7Osvy95tZl5k9ET4+FFl2hZn9Nnxckc/gZ6pvOEVDdYxYVf5uOpKRSfQ9Q7pJuIiUhilLWjOLAdcDvwfsBh41s01Z7v36fXe/aty2i4BPA+2AA4+F2x7KS/QzVIi56DNa6sNEP6iKXkRKQy4V/TlAh7tvc/ckcCtwSY77fzNwt7t3h8n9buCimYWaP4WY5yajJh6jLhFT142IlIxcEv0yYFfk9e6wbbw/MLMtZnabma2Y5raY2QYz22xmm7u6unIIa+YKmegh6L7pUaIXkRKRr5Ox/wGsdvdXEVTt357uDtz9Rndvd/f2tra2PIWVXSG7bkCJXkRKSy6Jfg+wIvJ6edh2hLsfdPfMzVK/CZyd67bFUPCKvj7BYfXRi0iJyCXRPwqsM7M1ZlYNXApsiq5gZidGXr4deDZ8fhdwoZktNLOFwIVhW1H1DqcKWtEvqEswNJpmKJku2DFERHI1ZVnr7ikzu4ogQceAje7+tJldB2x2903AR83s7UAK6AbeH27bbWafJfiyALjO3bsL8D6mJei6KWwfPcCLPUOsbWss2HFERHKRU7Zz9zuAO8a1XRt5fg1wzQTbbgQ2ziLGvEqmxhhJjR25grUQMkMs9x4eVqIXkaKruCtjCzkXfcaCumoAXjw8VLBjiIjkqgITfWZCs8L10TfXxjGCrhsRkWKr4ERfuIo+HquisSbO3sPDBTuGiEiuKjDRF24u+qiW+oQqehEpCRWX6As5F31US11CffQiUhIqMNEHFX1mCGShLKhLsLdnGHcv6HFERKZScYm+qy+4gLe1saagx2mpSzCYTNM7pBuQiEhxFbb/ooTc/PBOAO7/7QFq4lXc/qvCzsTQUh8OsewZOjKuXkSkGCquoi/0hGYZR66OVT+9iBRZ5SX6kcJOaJZxdBoEDbEUkeKqvERf4JkrM5pq49RXx9i6r7fgxxIRmUxFJXp3D7puCjjPTUaVGevXLOKXHQcLfiwRkclUVKIfSY0xmvY56aMHOH9dGy8cGGD3ocE5OZ6ISDYVlejnYvqDqAvWtQLwy44Dc3I8EZFsKivRj8zN9AcZ65Y0sqSphl/8VoleRIqnshL9HFf0Zsb5p7TywPMHGRvTFbIiUhxK9AV2/rpWugeSPLNXo29EpDhySvRmdpGZbTWzDjO7OsvyPzWzZ8xsi5n9t5mtiixLm9kT4WPT+G3nUt/wKPEqoy4Rm7NjnndK0E9/v/rpRaRIpkz0ZhYDrgcuBk4DLjOz08at9iug3d1fBdwGfCGybMjdzwgfb89T3DPSN5yisTaOmc3ZMZc21/KSpY384rddc3ZMEZGoXPowzgE63H0bgJndClwCPJNZwd3vjaz/EPDefAaZL/3DqTkZQ5+RmV9n2YJ67t3ayef+6xlObm3k8vUr5ywGEZFcum6WAbsir3eHbRP5IPCTyOtaM9tsZg+Z2Tsm2sjMNoTrbe7qKkz12ztH89yM99qXtLGooZofPb6HZGpszo8vIpUtrydjzey9QDvw95HmVe7eDlwOfMXM1mbb1t1vdPd2d29va2vLZ1hHzNX0B+NVx6t455nL6B5Ics+z++f8+CJS2XJJ9HuAFZHXy8O2Y5jZm4C/At7u7iOZdnffE/67DbgPOHMW8c5YKj3G0Gi6KIkeYG1bI+esWcQvOw7w1J6eosQgIpUpl0T/KLDOzNaYWTVwKXDM6BkzOxP4BkGS74y0LzSzmvB5K3Aekb79udQ/khlaWby54S96+QnUJmJ88adbixaDiFSeKRO9u6eAq4C7gGeBH7j702Z2nZllRtH8PdAI/Nu4YZSnApvN7EngXuDz7l6URF+MMfTj1SZivOYlbdy3tYvHdhwqWhwiUllyynrufgdwx7i2ayPP3zTBdg8Ar5xNgPnSNzy30x9M5NUnL+axHd186e6tfO9D5xY1FhGpDBVzZWxvpqKfw+GV2VTHq/iT167llx0HefB5TWEsIoVXMYm+bziFAQ1FTvQA7z13FUuba/jyPb8pdigiUgEqJtH3j4zSUBMnVjV3V8VOpDYR48OvWcsjL3Tz6PbuYocjIvNcxST6Yo2hn8hl56xkcUM1X525gRoAAAqeSURBVPtZR7FDEZF5rnQyX4Ed7E/S2lhd7DCAo1MjtK9ayF3P7OcLdz7H8oX1mhpBRAqiIir6vuFRDvSPsGxhXbFDOcb6kxdTm6jivq2a8ExECqciEv2v9/TgwPKF9cUO5Ri1iRi/u7aVZ/b2cqBvZOoNRERmoCIS/ZbdwZQDyxaUVkUPsH7NIqoMHtFJWREpkApJ9IdZWJ8oiaGV4zXVJnj5SS08tuMQw6PpYocjIvNQRST6J3f1lFy3TdT6NYsYGk3zH0++WOxQRGQemveJ/mD/CHsOD7G8xE7ERq1pbaCtqYbvhqNxRETyad4n+iP98yWc6M2M9WsW8eSuw2zZfbjY4YjIPDPvE/2Tuw9jBstaSjfRA5y5YiEtdQk+9O3N/Dr8cjo8mOTfn9jDnU/t5cHnDzKYTBU5ShEpR6V3djLPtuzu4ZS2RmoSsWKHMqm66hjf//C5fPCmzfzPbzzAG09dyj3P7GckcuvBU5Y08oMPv5pFDaVx4ZeIlId5XdG7O1t2H+ZVyxcUO5ScvOyEZn585XmcemIz9z7XybvOXs6PrzyPj7zhFP6wfTnbDwzwtn+6n433v3Dk6loRkanM64r+uX19HOhPcvqKlmKHkpNM8v6Ds5aTHnMSsSqeebGXE1vqOLGljtpEjO8+tINvP7id965fVdxgRaRszNuKfjQ9xl/8cAsL6hNc9IoTih3OtFSZkYgd/6N52QnN/GH7CnYfGuJr93awOXKRVVffCF+8aytv/If7+OPvbObGnz9PR2f/XIYtIiUqp4rezC4CvgrEgG+6++fHLa8BvgOcDRwE3u3u28Nl1wAfBNLAR939rrxFP4l/+lkHW3b38PX3nMWSptq5OOSceNXyBSxurOGWR3by7hsfYtXiemriMZ7v6mc0PcarT15MR2c/dz+zn7+54znWr1nEW08/iUSVkXZnbVsjpy9fQF318ecsUukxfrO/n0ODSc5etZDaCc5ruDtPv9gLBDc9z7av6Lodnf08tO0gg8k0jbVxFjdUs25pE6sW1RPP8oUmIvk1ZaI3sxhwPfB7wG7gUTPbNO7erx8EDrn7KWZ2KfB3wLvN7DSCm4m/HDgJuMfMXuLuBbkEdGzM2XZggIe2HeT6ezv4/bOWcfErTyzEoYpq2YI6rnr9Kdz7XCeHh0ZJjTlnrVzA757cSmtTDQC9w6M8sfMwj2zv5v/8+Kljto9XGaee2MzZqxaybmkjz3cOsGX3YZ56sYfh0eDkb10ixvnrWlm/ZhGvXNZCY22cjs5+tuzu4c6n9rHn8BAAZsF1AK9Z18YF61pZUF/NmDsvHBjggY4DPPD8QTonmMenOlZFc12C+uoY9dUx6qpjNFTHqQtfL19Yx8tOaGZtWyNLm2tYWF9NVYHuJ+DuJNNj7D40xAtdA7xwYIBtBwboHhhhbVsjp57YzJrWBpYvrKOlLoFZ8e9rIKUvlR7j4ECSfT3DdHT289vOfoZH0zTXJVhUn2BVawMntzawuLGG+kSsYP+/zd0nX8Hs1cBn3P3N4etrANz9byPr3BWu86CZxYF9QBtwdXTd6HqTHbO9vd03b948rTeSTI3xO399Dz1Dwb1h17Y1cPuV59Ec3iO2Uk9ejrnTMzRK5r/Pvt5hdnYPsvPgILsODTKadhIx48SWOpYvrGP5wnpqE0GV/d/Pdh5J6BkxM05Z0sgrljVTHY/R2TvMrkOD7OwePPIlkdFQE2dtWwNr2xpZ29ZIQ3WMkdQYfcMp9vUO09k3zPBomtG0k0yNkUyPkUyNMZoeY3g0Tc/QKGOR/55VBvGqyF8Adsw/RHOvha3RtjH3YH8ePPewbaJfgeALKE73wMgxccSqgr2bhcexY2MwjEJ9D0zx6zqzfVKAnVKYWIHCRFugWJPpY38nYlVGImaMpMaO+3zM4KSWOn559RtmdCwze8zd27Mty6XrZhmwK/J6N7B+onXcPWVmPcDisP2hcdsumyDIDcCG8GW/mW3NIbYJ7QBaPnVMUytwYDb7nM86pvH5bAN+muN+n5l6lXKi/0OT0+cztUk/o+1AUErPyIQjNEpm1I273wjcWKj9m9nmib7tRJ9PLvQZTU6fz9SK9RnlciZsD7Ai8np52JZ1nbDrpoXgpGwu24qISAHlkugfBdaZ2RozqyY4ubpp3DqbgCvC5+8CfuZB5/8m4FIzqzGzNcA64JH8hC4iIrmYsusm7HO/CriLYHjlRnd/2syuAza7+ybgW8C/mlkH0E3wZUC43g8IumpTwJWFGnGTg4J1C80T+nymps9ocvp8plaUz2jKUTciIlLedLWKiMg8p0QvIjLPzftEb2YXmdlWM+sws6uLHU+pMbMVZnavmT1jZk+b2ceKHVMpMrOYmf3KzP6z2LGUIjNbYGa3mdlzZvZseKGlhMzsE+Hv11NmdouZzem8LPM60Uemb7gYOA24LJyWQY5KAZ9099OAc4Er9Rll9THg2WIHUcK+Ctzp7i8DTkef1RFmtgz4KNDu7q8gGNRy6VzGMK8TPXAO0OHu29w9CdwKXFLkmEqKu+9198fD530Ev6BZr16uVGa2HPgfwDeLHUspMrMW4DUEo+9w96S7656Yx4oDdeF1RvXAi3N58Pme6LNN36AkNgEzWw2cCTxc3EhKzleAPwfGplqxQq0BuoB/Cbu3vmlmDcUOqlS4+x7gi8BOYC/Q4+65ziKSF/M90UuOzKwR+CHwcXfvLXY8pcLM3gp0uvtjxY6lhMWBs4Cvu/uZwADhhIYCZraQoCdhDcEsvg1m9t65jGG+J3pNwZADM0sQJPnvufuPih1PiTkPeLuZbSfo+nuDmX23uCGVnN3AbnfP/CV4G0Hil8CbgBfcvcvdR4EfAb87lwHM90Sfy/QNFc2CidW/BTzr7l8qdjylxt2vcffl7r6a4P/Pz9x9TquxUufu+4BdZvbSsOmNzLuJS2dlJ3CumdWHv29vZI5PVpfM7JWFMNH0DUUOq9ScB/wR8GszeyJs+0t3v6OIMUn5+QjwvbCg2gZ8oMjxlAx3f9jMbgMeJxjl9ivmeCoETYEgIjLPzfeuGxGRiqdELyIyzynRi4jMc0r0IiLznBK9iMg8p0QvMgkze7+ZnTSL7Veb2eX5jElkupToRSb3foLL1mdqNaBEL0WlRC8Vx8z+NJwX/Ckz+3hYdT8VWf4pM/uMmb0LaCe4EOgJM6szs+1m9gUz+7WZPWJmp4Tb3BSun9lHf/j088AF4fafmMv3KZKhRC8VxczOJrhqcz3B/Pt/DCzMtq673wZsBt7j7me4+1C4qMfdXwl8jWBmy8lcDfwi3P7L+XgPItOlRC+V5nzgdncfcPd+ggmmLpjmPm6J/Ks7KUnJU6IXgQUc+7sw1W3ePMvzVGYfZlYFVOctOpFZUqKXSvML4B3hTIINwDuBnwBLzGyxmdUAb42s3wc0jdvHuyP/Phg+3w6cHT5/O5CYZHuROTWvZ68UGc/dHzezm4BHwqZvuvujZnZd2LYHeC6yyU3ADWY2xNFumoVmtgUYAS4L2/4Z+HczexK4k+DmGwBbgHTYfpP66aUYNHulyDSENyBpd/cDxY5FJFfquhERmedU0YuIzHOq6EVE5jklehGReU6JXkRknlOiFxGZ55ToRUTmuf8Po8UNOotWWzUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median % of icu patients ventilated: 0.43 (0.16 to 1.02)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(model_v5.frac_icu_ventilated)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "43fae95bc84e4bf7b54549217181ac10",
      "c8171b37493d49009fb83e9c38aa98c0",
      "0ada2ae37f2044d2b375e92ed98ff690",
      "c96aa59bfc3c4ec4880edf95da35f1f4",
      "e6ddfdecbe834c0895341419c620fdde",
      "1444b1248238448fb344308968ef1c52",
      "2c83cc02c78d4089981e7099ef15640c",
      "6c8cd09e62b14021a08c49971d91e74a"
     ]
    },
    "colab_type": "code",
    "id": "39h8180y_lla",
    "outputId": "4649f3a1-3f17-4a71-aae1-c55ed001c9c8"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "43fae95bc84e4bf7b54549217181ac10",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median % icu patients that need ventilation at some point while in the ICU: 0.51 (0.22 to 1.03)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(model_v5.icu_receive_ventilation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 361,
     "referenced_widgets": [
      "29eb8af8eb2145718c1877d2cf4bd915",
      "446ed9fc65ce48a48555e1ea5db4e7b5",
      "e8d4030896a44842a780da8e2ebd2b55",
      "1d944682c0d84fd894793fd20e49a5a3",
      "b7103a63ca3b41b7a760bd2e498155ad",
      "b074f29ef2dd413393e1a6c917cc4917",
      "d13f3fd6be4c40bfa52577750c8ac171",
      "fed3c71ee77c4db89eb94e52535778a6"
     ]
    },
    "colab_type": "code",
    "id": "bSzJbhST_llk",
    "outputId": "1c039bc2-b012-495e-ff2a-bfa012ab05ce"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "29eb8af8eb2145718c1877d2cf4bd915",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=1000.0), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median adjustment to the % of icu patients ventilated at some point to get the % currently ventilated: 0.88 (0.51 to 1.52)\n"
     ]
    }
   ],
   "source": [
    "show_marginal(model_v5.icu_ventilation_adjustment)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mJxfAvru_llw"
   },
   "source": [
    "# Review"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
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    "My original question was:\n",
    "\n",
    "> How many ventilators will be needed for COVID patients in El Paso county in May?\n",
    "\n",
    "We broke it down as follows:\n",
    "\n",
    "- **\\# ventilators needed [Result: 44.82 (7.12 to 608.06)]** =\n",
    "  - max # icu patients [Result: 106.50 (22.00 to 1174.00). Source: [Columbia model](https://github.com/shaman-lab/COVID-19Projection)] *\n",
    "  - % of icu patients ventilated [Result: 0.43 (0.16 to 1.02)] =\n",
    "      - \\% icu patients that need ventilation at some point while in the ICU [Result: 0.51 (0.22 to 1.03). Source: combination of [PabloStafforini et al.](https://pandemic.metaculus.com/questions/4154/what-portion-of-in-hospital-patients-with-covid-19-in-el-paso-county-will-require-invasive-ventilation/#comment-28155)] and Metaculus community prediction*\n",
    "      - icu-ventilation adjustment [Result: 0.88 (0.51 to 1.52). Source: guess.]"
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    "# Exercises for the reader\n",
    "\n",
    "Some questions to help you think through and extend my model:\n",
    "\n",
    "1. What did I change about the model at each step and how did that affect my prediction? Do you think the change in my prediction is likely to be an improvement?\n",
    "\n",
    "2. How could I decompose the question further or use better data/submodels to make a better prediction?\n",
    "  \n",
    "  a. How could I make a data/model based prediction for `icu-ventilation adjustment` instead of making a guess?\n",
    "\n",
    "  b. How could I make better use of the Metaculus community predictions to estimate `% icu patients that need ventilation at some point while in the ICU`? Does it make sense to sample from each of the 2 Metaculus questions independently of the other?\n",
    "\n",
    "3. What assumptions does the model make that might be unwarranted?\n",
    "  \n",
    "  a. What does the model assume about the relationship between the number of patients in the ICU on a given day, and the proportion of those patients who need to be ventilated?\n",
    "\n",
    "4. The final model is currently extremely uncertain.\n",
    "  \n",
    "  a. Why?\n",
    "\n",
    "  b. Is that uncertainty warranted?\n",
    "\n",
    "  c. How could you reduce it in a reasonable way?"
   ]
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